Mutual inductance calculation between arbitrarily positioned rectangular filaments

Abstract

Abstract. The mutual inductance between the transmitted and received coils is an important parameter in the inductively cou-pled wireless power transmission system. The relative position between the linked coils may be arbitrary according to theapplications. In this paper the analytical calculation of the mutual inductance between two arbitrarily positioned rectangu-lar filaments is proposed based on a more general expression of mutual inductance calculation of two arbitrarily positionedstraight filaments than Grover’s. The calculation results are validated by using the finite element simulation tools. The previouspublished approximation methods for square coils in the coaxial, lateral misalignment or angular misalignment situations areverified that they are accurate when the two coils’ relative distances are large.Keywords: Mutual inductance, rectangular filament, arbitrary position 1. IntroductionIn the wireless power transmission system, the power is transferred from the transmitted coil to thereceived coil through the inductively coupled method whose coupled coefficient and the transfer effi-ciency are related to the mutual inductance between the two coils [1]. In addition to the inductivelycoupled power transmission application, the mutual inductance is also a basic parameter in the applica-tions like the electromagnetic induction sensors[2], and the electrical machines [3].The mutual inductance is related to the coils’ shapes,sizes, and relative positions [4]. The commonlyused shapes of the coils are circular or rectangular/square. No matter what shapes are, the relative posi-tionwillbecoaxial,coplaner,perpendicularorevenarbitraryaccordingtotheapplications.Furthermore,in some applications the relative position will be changed with the time. A typical example is the ap-plication of the wireless power transmission for the capsule endoscope, where the received coils insidethe body are movable irregularly [5]. Although two coaxial coils are needed in some applications, thelateraland/orangularmisalignmentswillbeinevitable.Insummary,itisnecessarytoanalyzethemutualinductancein the most general situation that the two coils are arbitrarily positioned.The mutual inductance of the